There's a fascinating prophecy in Isaiah that clearly points to an upcoming Gentile priesthood within the New Testament Church. This is a good verse to keep in mind when talking to Protestants, who strongly resist the idea of a New Testament sacrificial priesthood:
Isaiah 66: 20 And they shall bring all your brothers from all the nations as an offering to the Lord, on horses and in chariots and in litters and on mules and on dromedaries, to my holy mountain Jerusalem, says the Lord, just as the Israelites bring their grain offering in a clean vessel to the house of the Lord. 21 And some of them also I will take for priests and for Levites, says the Lord.
To fully appreciate what Isaiah is saying, recall that in the Old Testament under the Mosaic Law, the priesthood was hereditary, tied strictly to the biological lineage of Levi. Within the Tribe of Levi, only Aaron's biological sons were priests, while the rest of the Levites were assistants, which we would call Deacons (see here). So for Isaiah to say there will come a time when men from 'every nation' will be called to the priesthood, that's very radical.
We would certainly expect Protestants to object to this text, but the good news is that they actually agree with this prophecy! The Reformed Protestant tradition teaches within the Westminster Standards on Form of Church Government:
That the ministers of the gospel have as ample a charge and commission to dispense the word, as well as other ordinances, as the priests and Levites had under the law, proved, Isaiah lxvi. 21. Matt. xxiii. 34. where our Saviour entitleth the officers of the New Testament, whom he will send forth, by the same names of the teachers of the Old.
To administer the sacraments. To bless the people from God, Numb. vi. 23, 24, 25, 26. Compared with Rev. i.4, 5, (where the same blessings, and persons from whom they come, are ex mentioned,) Isa. lxvi. 21, where, under the names of Priests and Levites to be continued under the gospel, are meant evangelical pastors, who therefore are by office to bless the people.
What is ironic here is that the Reformed Protestant tradition basically makes the case for the Catholic priesthood for us, but the Reformed Protestant refuses to admit it (or doesn't want to deal with it).
Another noteworthy prophecy is seen when Jesus goes in to cleanse the Temple: "And he entered the temple and began to drive out those who sold, saying to them, “It is written, ‘My house shall be a house of prayer,’ but you have made it a den of robbers.”" This quote is taken from Isaiah 56, which says:
6 “And the foreigners who join themselves to the Lord, to minister to him, to love the name of the Lord, and to be his servants, everyone who keeps the Sabbath and does not profane it, and holds fast my covenant: 7 these I will bring to my holy mountain, and make them joyful in my house of prayer; their burnt offerings and their sacrifices will be accepted on my altar; for my house shall be called a house of prayer for all peoples.”
Again, the same theme as Isaiah 66:21 above. Those from all nations, no longer only the Levites, will be welcome to minister to God in liturgical worship, including offering sacrifices. This is no small prophecy, but rather one which the Christian Church is heavily based upon for our own worship even today, in the Holy Sacrifice of the Mass (see here).